Consistent analytical approach for the quasi-classical radial dipole matrix elements

A consistent analytical approach for calculation of the quasi-classical radial dipole matrix elements in the momentum and coordinate representations is presented. Very simple but relatively precise expressions for the matrix elements are derived in both representations. All analytical expressions contain only one special function-the Anger function and its derivative. They generalize and increase the accuracy of some known quasi-classical expressions. The small difference between the two forms of the expressions for the dipole matrix elements indicates the applicability of the simple expressions given by the consistent quasi-classical approach even for low atomic states.